Extended constitutive laws for lamellar phases

Chi-Deuk Yoo, Jorge Vinals
Abstract:
Classically, stress and strain rate in linear viscoelastic materials
are related by a constitutive relationship involving the viscoelastic
modulus G(t). The same constitutive law, within Linear Response
Theory, relates currents of conserved quantities and gradients of
existing conjugate variables, and it involves the autocorrelation
functions of the currents in equilibrium. We explore the consequences
of the latter relationship in the case of a mesoscale model of a
block copolymer, and derive the resulting relationship between viscous
friction and order parameter diffusion that would result in a lamellar
phase. We also explicitly consider in our derivation the fact that the
dissipative part of the stress tensor must be consistent with the uniaxial
symmetry of the phase. We then obtain a relationship between the stress
and order parameter autocorrelation functions that can be interpreted as
an extended constitutive law, one that offers a way to determine them
from microscopic experiment or numerical simulation.